Model Of Flexible Manipulator Research Articles

Configuration reconstruction and all-joint synchronous measurement based on vision for segmented linkage manipulator of rigid-flexible dual-arm space robot

A rigid-flexible dual-arm space robot offers promising potential for on-orbit operation due to complementary strengths of its rigid and flexible manipulators. The rigid manipulator has the advantage of large payload capacity and high motion accuracy. The segmented linkage flexible manipulator is ideal for maneuvering in narrow, unstructured environments like internal satellite inspections and maintenance, due to its flexibility and slender body. However, there are inevitable tracking errors due to the multiple cable-driven mechanisms in the flexible manipulator. It’s difficult to get the configuration and end pose of flexible manipulator without adding external sensors. To address these issues, this paper presents a method for configuration reconstruction and all-joint synchronous measurement of the flexible manipulator. The flexible manipulator is captured by the stereovision system mounted on the rigid manipulator. The links’ equivalent center points are recognized by central moment method and edge line extraction method based on the natural characteristics. Joint-to-link kinematic model of flexible manipulator is established to measure joint angles and reconstruct configuration. Several simulations and experiments are carried out to validate the proposed method. The experimental results showed links’ average measurement position errors were less than 13 mm and joint angles reconstructed using the proposed method had an error of approximately 0.35°. These results demonstrate the accuracy and robustness of the proposed method.

An Alternate Perspective on Modeling and Control of a Flexible Manipulator: Case Study of a Curvature Control Manipulator Dynamics

Abstract The flexible and adaptable nature of continuum soft robots makes them applicable to a wide range of operations not easily obtainable with conventional rigid-body robots. Thus, soft robots can be used in various operations such as manipulation tasks, minimally invasive surgery operations, robotic rehabilitation/wearable devices, inspection, and surveillance tasks. Unfortunately, the continuous nature of these robotic systems leads to significant modeling and control challenges. Presently, there are various modeling perspectives. However, a detailed review shows that current models are often characterized by problems such as high computational costs, quasi-static assumptions, imprecise inclusion of boundary conditions, spillover instability, etc. These problems limit the accuracy of the resulting model, requiring more effective modeling and control strategies. Therefore, this paper is aimed at improving the state of the art and science of current models by providing more effective strategies for the problems encountered. In this regard, the dynamic modeling of a two-link tendon-driven flexible manipulator based on hybrid parameter multibody system methodology will be presented to demonstrate these strategies. Using the model, path-planned dynamic controls based on pole placement, linear quadratic regulator, and sliding mode control methods will be implemented for a continuous time-varying path. Also, a comparison of the performance of the control methods, in addition to parametric studies for the optimal tendon connection points, will be presented. Results showed that the benefits of the modeling approach and strategies employed led to a highly accurate, real-time performance for the complex motions of the manipulator system.

Research on the grasping characteristics of composite-driven double-finger flexible manipulator.

Aiming at the flexible manipulator grasping complex target parts of different shapes, a double-finger flexible manipulator model is proposed. The manipulator is composed of a flexible mechanical finger, a driving component and a position compensation mechanism. It imitates the motion characteristics of human finger joints and follows the principle of double-fingered grasping. According to the structural characteristics of the target contour, the grasping features of the target contour are extracted. Through the motion principle of the flexible manipulator, the kinematic model of the envelope clamping process of the manipulator target is carried out. Finally, the flexible manipulator experimental platform is built to verify the grasping characteristics of the flexible manipulator target. The results show that the manipulator can realize the adaptive grasping of cylinder and cuboid parts, which have high grasping reliability and stability.

Dynamic research on winding and capturing of tensegrity flexible manipulator

With the rapid development of social intelligence, flexible manipulator has become a typical representative of the intelligent era. However, due to the strong nonlinearity brought about by the high flexibility of the flexible manipulator, as well as the nonsmooth problems it faces during operation such as cable slacking and contact, it poses challenges to its modeling and dynamic analysis. Considering the above difficulties, this article first proposes a modeling strategy for flexible manipulator based on the theory of tensegrity, which can establish a highly flexible manipulator model. Then, based on the theory of nonsmooth multibody systems, a nonsmooth mathematical formula for cable slacking and contact is established to address the nonsmooth phenomena. Finally, a variable cross-section tensegrity flexible manipulator is designed, and the dynamic characteristics of winding and capturing are analyzed. Numerical results validate the effectiveness of the proposed method.

Study on dynamic modelling and vibration analysis of single-link flexible manipulator

In this study, SimMechanics-based dynamic modeling and vibration analysis of a single-link flexible manipulator are studied. A flexible beam model is set up for modeling the manipulator. Transient analysis is performed to obtain the endpoint acceleration vibration responses of the manipulator moved with different motion profiles. Both the experimental and simulation acceleration results are presented for different cases. The root means square (RMS) values of the acceleration responses are calculated to evaluate the compatibility performance in verifying the simulation results with the experimental results. It has been observed that the results match each other successfully for different cases. The reliability of the SimMechanics-based dynamic modeling method of manipulators is discussed with the experimental results.

Robust deflection control and analysis of a fishing rod-type flexible robotic manipulator for collaborative robotics

Due to high-speed operation at low inertia, flexible manipulators are becoming more and more popular in today’s world. These manipulators produce excessive vibration, which must be reduced using an efficient control technique for the manipulator to function well. In the present study, a flexible manipulator model with a single link is built in such a manner that it can be considered as a flexible fishing rod. The free end of the flexible rod has a provision for applying a payload, which serves to give a deflection of the flexible rod. A lumped parameter method is adopted for modelling the flexible rod as well as the string using the Sim-Mechanics tool in MATLAB. Simulations were carried out for sudden and sinusoidal loading. It has been found that the flexible link produces excessive vibration under both sudden and sinusoidal loading. A proportional integral derivative (PID) controller is used to suppress the excessive vibration generated in the simulation model. Four different locations (Location 1: 15 cm; Location 2: 30 cm; Location 3: 45 cm; and Location 4: 60 cm) are selected for controller positioning. Simulation revealed that the minimum deflection was observed at location 4, i.e., at the tip for both sudden and sinusoidal loading. The developed model is validated using two loading conditions, viz., the beam’s self-weight and a point load of 30 N at the free end. It has been found that the simulation results resemble the analytical results with an error of 0.44% and 0.36% for both the loading conditions.

Моделирование динамики упругих звеньев исполнительных механизмов манипуляторов без обращения их матриц масс

In recent scientific literature, much attention is paid to the optimal modeling of elastic dynamical systems. The relevance of these studies is dictated by the ever-increasing demand in the control theory of high-precision robotic manipulators and automatic mechanisms, which consists in the need for continuous adjustment of the movement of their executive bodies in real time, with account for the flexibility of the constituent links of these systems. The generalized Newton --- Euler method formulated in this regard served as a reliable platform for a subsequent progressive modification of dynamic analysis for a wide class of elastodynamic systems. The purpose of the study is to improve the existing computational algorithms to accelerate the computational process of dynamic analysis of flexible manipulators. In this regard, relying on symbolic-iterative calculus, we formulated and solved the mixed dynamic problem of the manipulators without inverting their mass matrices. Furthermore, we modified the Newton --- Raphson method, intended for a numerical integration of the Newton --- Euler equations of motion. Finally, we dynamically calculated the spatial five-elastic link manipulator by comparing the speed of computational processes carried out at constant accuracy of the problem modeling, and assessed the efficiency of the method of dynamic analysis of the manipulators. In this study, we introduce an advanced method of dynamic modeling of flexible manipulators without the well-known procedure of their mass matrices inversion

Study on modeling and dynamic performance of a planar flexible parallel manipulator based on finite element method.

The application of a high-speed parallel manipulator necessitates the adoption of a lightweight design to reduce dead weight. However, this increases the elastic deformation of certain components, affecting the dynamic performance of the system. This study examined a 2-DOF planar flexible parallel manipulator. A dynamic model of the parallel manipulator composed of fully flexible links was established using a floating reference coordinate system and a combination of the finite element and augmented Lagrange multiplier methods. A dynamic analysis of the simplified model under three driving torque modes showed that the axial deformation was less than the transverse deformation by three orders of magnitude. Further, the kinematic and dynamic performance of the redundant drive was significantly better than that of the non-redundant drive, and the vibration was well suppressed in the redundant drive mode. In addition, the comprehensive performance of driving Mode 2 was better than that of the other two modes. Finally, the validity of the dynamic model was verified by modeling via Adams. The modular modeling method is conducive to the extension to other models and programming. Furthermore, the dynamic model of the established fully flexible link system can aid in optimizing the lightweight design and dynamic performance of the parallel manipulator.

Dynamic Modeling and Vibration Suppression for Two-Link Underwater Flexible Manipulators

This paper proposes a composite controller (CC) to improve the accuracy of trajectory tracking and suppress the vibration of two-link underwater flexible manipulators. A dynamic model of the flexible manipulators considering hydrodynamic force is established by combining the Lagrange equation and Morison formula. Then, the dynamic model is divided into a flexible dynamic subsystem and rigid dynamic subsystem, and a decomposed dynamic control strategy is presented for the two subsystems. In particular, an adaptive fuzzy sliding mode control scheme (AFSMC) with good robustness to compensate for uncertain factors is designed to track the joint trajectory and suppress vibration. Next, the trajectory tracking control of two-link underwater flexible manipulators is simulated to investigate the performance of the framework. The results show that the hydrodynamic force and flexible deformation markedly affect the input torque of the joint, and the traditional sliding mode controller (SMC) is superior to proportional integral derivative (PID) control in managing hydrodynamic force disturbance and inferior in suppressing flexible vibration. The proposed composite controller based on adaptive fuzzy sliding mode control CC(AFSMC) is more effective in restraining the vibration of flexible manipulators and resisting hydrodynamic force disturbance than PID and CC(SMC).

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are vibration control of flexible links and trajectory control of flexible robots. A brief, yet, significant review is provided that addresses these two issues. Methods: For vibration control of flexible links, possibilities of the use of passive and active damping methods are explored in the literature. After that, the effect of proper trajectory planning to ensure positional accuracy at the end-effector is studied. Findings: After a review of 181 research papers from the year 1970 to 2021, it has been found that the vibration suppression of flexible links can be achieved through the application of viscoelastic materials, piezoelectric materials, and optimum trajectory planning. Recent trends in research in the area of flexible manipulators show that an optimal trajectory can significantly help in reduction of link vibrations and achievement of positional accuracy simultaneously. Novelty: The novelty of the present work lies in exploring the possible application of passive and active damping control methods for vibration suppression of flexible link manipulators. Besides that, the survey also highlights how well planned trajectory may help achieve accurate tip positioning of flexible robots. Keywords: Flexible manipulator; viscoelastic damping; active vibration control; trajectory planning and control

Measurement and modeling of a flexible manipulator for vibration control using five-segment S-curve motion

User designed manipulators are widely used in industry as a part of automation. The design of lighter robotic arms is required for less energy consumption. Joints, structural features, and payload affect the dynamic behavior of manipulators. Even if the arms have sufficient structural rigidity, joints, or payloads further increase their flexibility. These factors should be considered at the design stage. Flexibility causes vibrations, and these vibrations negatively affect robot repeatability and processing speed. Reducing the vibration levels of flexible manipulators is an attractive issue for engineers and researchers. Accurate estimation of the mathematical model of flexible manipulators increases the success of vibration control. In this paper, the modeling and experiments for vibration control of a single-axis flexible curved manipulator with payload are considered. The experimental system is introduced to collect vibration responses synchronously at the tip of the curved manipulator for angular velocity input. The mathematical model of the manipulator is estimated using the continuous-time system identification (CTSI) method with a black-box model based on the experimental input/output (I/O) signals. A five-segment S-curve motion input based on the modal parameters is designed to suppress residual vibrations. Vibration control is successfully performed for different deceleration times of the designed S-curve motion input. The results showed that the residual vibrations from experiments and predicted models matched well for different cases depending on payload, angular position, and motion time.

Dynamic modelling and control of flexible link manipulators: methods and scope- Part-1

Objectives: This paper addresses two key issues in the area of flexible robotics. The issues are dynamic modelling and control of flexible link robots. A brief, yet, significant review is provided that addresses these issues. Methods: The various approaches used by researchers for dynamic modelling and control of flexible robots are presented. Besides that, methods used for achieving optimal control are also discussed. Findings: After a review of 153 research papers from the year 1975 to 2021, it has been found that a good dynamic model of flexible manipulator helps in reducing the control and computational efforts. Recent trends in research in the area of flexible manipulators are towards the use of sliding mode control and vision-based control techniques. Novelty: Inclusion of the effect of torsional vibrations besides lateral vibrations on the positional accuracy of flexible manipulators makes the current research work novel. Keywords: Flexible manipulator; modelling; dynamics; control

Elastostatic Modeling of Multi-Link Flexible Manipulator Based on Two-Dimensional Dual-Triangle Tensegrity Mechanism

Abstract The paper deals with the elastostatic modeling of a multi-link flexible manipulator based on the two-dimensional (2D) dual-triangle tensegrity mechanism and its nonlinear behavior under external loading. The main attention is paid to the static equilibriums and the manipulator stiffness behavior under the loading for the arbitrary initial configuration. It was proved that there is a quasi-buckling phenomenon for this manipulator while the external loading is increasing. In the neighborhood of these configurations, the manipulator behavior was analyzed using the enhanced virtual joint method (VJM). A relevant simulation study confirmed the obtained theoretical results.

Modeling and motion control of an octopus-like flexible manipulator actuated by shape memory alloy wires

Soft robots are concerned by researchers due to several characteristics, such as high adaptability in complex unstructured environments, safe interaction with environments, and a high degree of dexterity. The deformability and dexterity of the octopus arm are remarkable and interesting for the development of bioinspiration soft robots. In this study, we proposed a biomimetic flexible manipulator actuated by shape memory alloy (SMA) wires and its PI controller, and evaluated its performances with focused experiments. This study aims to find out the advantages of the developed manipulator actuated by SMA wires. We designed the bionic structure to achieve flexible bending in 3D space based on the analysis of the octopus muscle structure. Then we built the mathematical models that described the relationship between the bending angle and the driving parameters. Surprisingly, the soft movement capacity of the bionic manipulator was investigated at different heating voltages and PWM duty cycles by the PI controller based on the self-sensing resistance feedback. The soft manipulator was able to bend flexibly with the maximum bending angle of 60°. Compared to the traditional soft arm, the soft manipulator has higher accuracy, with the error of the deflection angle less than 5° and the errors of bending angles less than 2°.

Dynamic Modeling of Planar Multi-Link Flexible Manipulators

A closed-form dynamic model of the planar multi-link flexible manipulator is presented. The assumed modes method is used with the Lagrangian formulation to obtain the dynamic equations of motion. Explicit equations of motion are derived for a three-link case assuming two modes of vibration for each link. The eigenvalue problem associated with the mass boundary conditions, which changes with the robot configuration and payload, is discussed. The time-domain simulation results and frequency-domain analysis of the dynamic model are presented to show the validity of the theoretical derivation.

Control Method of Flexible Manipulator Servo System Based on a Combination of RBF Neural Network and Pole Placement Strategy

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator’s flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller’s parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange’s principle. Then, the system’s control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy.

The Study of Dynamic Modeling and Multivariable Feedback Control for Flexible Manipulators with Friction Effect and Terminal Load.

The flexible manipulato is widely used in the aerospace industry and various other special fields. Control accuracy is affected by the flexibility, joint friction, and terminal load. Therefore, this paper establishes a robot dynamics model under the coupling effect of flexibility, friction, and terminal load, and analyzes and studies its control. First of all, taking the structure of the central rigid body, the flexible beam, and load as the research object, the dynamic model of a flexible manipulator with terminal load is established by using the hypothesis mode and the Lagrange method. Based on the balance principle of the force and moment, the friction under the influence of flexibility and load is recalculated, and the dynamic model of the manipulator is further improved. Secondly, the coupled dynamic system is decomposed and the controller is designed by the multivariable feedback controller. Finally, using MATLAB as the simulation platform, the feasibility of dynamic simulation is verified through simulation comparison. The results show that the vibration amplitude can be reduced with the increase of friction coefficient. As the load increases, the vibration can increase further. The trajectory tracking and vibration suppression of the manipulator are effective under the control method of multi-feedback moment calculation. The research is of great significance to the control of flexible robots under the influence of multiple factors.

Towards accurate robot modelling of flexible robotic manipulators

As industry heads to an era of high productivity and energy efficiency, the manufacturing of robotic manipulators moves far from the traditionally heavy and stiff structures. Therefore, rigid body dynamic models become obsolete and the need for new dynamic models accounting for the flexibility of industrial manipulators emerges. To this end, a physics-based approach considering the flexibility of robots’ links and gearboxes is presented. In particular, this paper intends to provide a framework for modelling flexible robotic structures’ towards increasing their accuracy. The robot components’ elasticity is introduced in a lumped parameters model by pairs of springs and dampers, the number of which is affected by the target of keeping the computational effort and run time of the simulation at levels allowing for the integration of the model in industrial environments. Finally, the proposed model considers the activation of the robots’ Digital Twins aiming to enable the use of the model in a series of applications e.g. predictive maintenance, energy efficiency optimization etc.

Vibration control of coupled Duffing oscillators in flexible single-link manipulators

Motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of the flexible manipulators and thus should be suppressed to achieve tip positioning accuracy and high-speed operation. Because of the structural flexibility, the dynamics of the flexible manipulator can be described by coupled Duffing oscillators when considering the inherent structural nonlinearity of the flexible link into the dynamic modeling. However, little research has been focused on addressing the dynamic coupling issue in the nonlinear modeling of flexible-link manipulators using coupled Duffing oscillators. This article presents coupled Duffing oscillators for the nonlinear modeling of flexible single-link manipulators and then proposes a control method for suppressing the nonlinear vibrations of the coupled Duffing oscillators. Simulated and experimental results obtained from a flexible single-link manipulator test bench are in good agreement with the proposed nonlinear modeling and also demonstrate the effectiveness of the proposed control techniques for vibration suppression of the flexible manipulator.

Kinematic modeling of a class of n-tendon continuum manipulators

Flexible manipulators become widely used in industrial and medical fields due to their high dexterity compared with traditional discrete manipulators. However, in existing kinematics models of flexible manipulators without extension ability, the inverse kinematic (IK) analytical solution including the end-effector position and pose cannot be obtained. In this paper, a design example of a class of n-tendon continuum manipulators is presented. Based on the constant curvature hypothesis, a unified solution for solving the coupling relationship among tendons is derived. Combined with the Denavit-Hartenberg (D-H) method, the Taylor Series and the quaternion, the forward and inverse models are established, and an approximate analytical solution to the IK is derived. Simulations show the proposed IK solution has a good performance in accuracy and efficiency. A two-dimensional plane experiment and a three-dimensional space experiment are implemented. The average position errors of the two validation experiments respectively account for less than 2.0% and 3.5% of the total manipulator length, and the average pose errors are respectively no more than 0.8° and 2.5°.